The generation of different states of light is of fundamental interest in quantum optics and enables powerful applications such as the increase in sensitivity achieved in the interferometric detection of gravitational waves through the use of squeezed states with reduced uncertainty [1]}. Likewise, the generation of approximate Gottesman-Kitaev-Preskill (GKB) states [2]} is needed to implement fault-tolerant quantum computing on photonic setups [3]}. In this context, quantum two-photon states are commonly produced by exploiting the nonlinear response of some materials to coherent laser illumination through processes such as four-wave mixing [4]} and parametric down-conversion [5]} assisted by bright modes in optical cavities. In a radically different approach, free electrons have been identified as a promising tool to generate quantum light states [6]}, [7]}. In addition to the nanometer precision with which electron beams (e-beams) can be focused on an optical cavity, they are advantageous with respect to external light excitation in that they can interact with strongly-confined dark modes because they act as broad sources of evanescent fields [8]}.
